Electric-Field-Induced Paths in Multiferroic ${\mathrm{BiFeO}}_3$ from Atomistic Simulations

Properties of ${\mathrm{BiFeO}}_3$ under an electric field are simulated using an ab initio-based approach. Complex paths and anomalous phenomena occur, depending on the direction of the field. Examples of such phenomena are the rotations of the polarization and of the axis about which the oxygen octahedra tilt; isostructural transitions; disappearance and reappearance of the tilting of the oxygen octahedra; and reentrance into specific crystallographic classes.The magnetic order parameter is not always perpendicular to the polarization, especially when the tilting of the oxygen octahedra disappears. The governing “rule” is that the magnetic order parameter remains orthogonal to the axis about which the oxygen octahedra tilt.

Figure 1

Local modes [panel (a)], AFD-related quantity [panel (b)] and antiferromagnetic moment [panel (c)] of ${\mathrm{BiFeO}}_3$ at 10 K as a function of the magnitude of an electric field applied along the $[00\overline{1}]$ direction. Insets of panels (a) and (b) show the angle between the polarization and the [111] direction, and the angle between $\omega$ and the [111] direction, respectively. The inset of panel (c) displays the angle between $\mathbf{L}$ and $\mathbf{P}$ (via open squares) and the angle between $\mathbf{L}$ and $\omega$ (via open circles).

Figure 2

Panels (a)–(c) and (d)–(f): Same as Fig. 1 but for a field applied along the $[1\overline{1}1]$ and $[\overline{1}\overline{1}1]$ direction, respectively.

Figure 3

Same as Fig. 1 but for a field applied along the $[\overline{1}\overline{1}0]$ direction.